sort of in order:
a) since this is the Napoleonic era, destroying your opponent's army should be the goal --- its not the Seven Years War

. Of course sometimes taking key resources is the easiest way to destroy their ability to fight
b+c) these link. Ok this is a complex concept but key to good play. The basics are simple. Each 'army' has an 'army HQ' stack on 0+ 'corps'. Any formation in an 'army' can support another in combat in a neighbouring province. Now there are rules for which is most likely to respond and the 'army HQ' stack gets a particular bonus. So if Napoleon, plus some well chosen elite force is your reserve, he's highly likely to respond.
--- rather than burden you with details, basically a corps etc is more likely to react if: the journey time is short (so say the provinces are connected by a major road); the opposite applies, so reacting across an unbridged major river, into a wooded-hills province is very unlikely; the higher the initiative rating of the immediate commander and the commander in chief (Napoleon again); if the stack is activated; if the stack is an offensive stance
It also is tested each hour after the first, so a support corps may contribute in one round and fail the test in another.
Its a critical part of good AGE play, but sooner or later it will fail you, so you can't rely on it. Especially if you are on the defensive or plagued with poor commanders
d) watch out for command limits, try not to exceed these. Also huge armies may have supply and movement penalties. There is though another tricky rule which is stack targetting. Basically once battle commences each separate stack picks an opposing stack (often both sides will have more than one), if you have too many small stacks there is a risk these might be targetted by a powerful enemy stack and overwhelmed (think of it as a subset of a battle where command or terrain has allowed the enemy to isolate a small detachment). This is bad news. So the advice is to follow the goldilocks principle .... if I am going to have stacks in the same province I make sure each is as large as I can safely make it.